Real Tunneling Solutions and the Hartle-Hawking Wave Function

Abstract

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing ``momentum'') at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely; consequently, such an instanton will contribute to the wave function at only one or a few isolated spatial geometries. I show that these geometries are the extrema of the Hartle-Hawking wave function in the semiclassical approximation, and provide some evidence that with a suitable choice of time parameter, these extrema are the maxima of the wave function at a fixed time.

10 pages, LaTeX, UCD-92-30

References in corpus (2)

• The Sum over Topologies in Three-Dimensional Euclidean Quantum Gravity
• Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

Cited by in corpus (8)

• Quantum Gravity: a Progress Report
• Some implications of signature-change in cosmological models of loop quantum gravity
• Spacetime foam: a review
• Tunelling with a Negative Cosmological Constant
• Peaks in the Hartle-Hawking Wave Function from Sums over Topologies
• Comment on "Failure of standard conservation laws at a classical change of signature"
• On the Growth of the Number of Hyperbolic Gravitational Instantons with respect to Volume
• A Note on Real Tunneling Geometries